This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By construct...This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument.The first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth conditions.The second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type conditions.In addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true solutions.Lastly,we carry out some numerical experiments to support the theoretical results.展开更多
This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM meth...This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.展开更多
As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimizat...As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.展开更多
Calculations of the ElectroMagnetic(EM) response produced by a large horizontal loop placed over layered medium are rather complex because its integral expression contains the product of two Bessel functions and has a...Calculations of the ElectroMagnetic(EM) response produced by a large horizontal loop placed over layered medium are rather complex because its integral expression contains the product of two Bessel functions and has a divergent term. In this paper, an improved fast Hankel and Gaver-Stehfest transforms are introduced to solve the strong-oscillation and slow-decay properties of the integrand, where one Bessel function in the product is substituted by a carefully chosen polynomial of high accuracy and the other used as the digital filter coefficients in the convolution integral. Comparisons prove the validity and the efficiency of the proposed method.展开更多
This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solutio...This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solution for homogeneous earth and it is used to calculate the secondary electric field in the inhomogeneous Helmholtz Equation. Calculation of Helmholtz Equation is carried out using the finite element method. Validation of this modeling is conducted by comparison of numerical results with 1D analytical response for the case of homogeneous and layered earth. The comparison of CSAMT responses are also provided for 2D cases of vertical contact and anomalous conductive body with the 2D magnetotelluric (MT) responses. The results of this study are expected to provide better interpretation of the 2D CSAMT data.展开更多
Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data ...Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data for the detection of DHIs, new methods have been investigated. Marine controlled source electromagnet (MCSEM) or Sea bed logging (SBL) is new method for the detection of deep target hydrocarbon reservoir. Sea bed logging has also the potential to reduce the risks of DHIs in deep sea environment. Modelling of real sea environment helps to reduce the further risks before drilling the oil wells. 3D electromagnetic (EM) modelling of seabed logging requires more accurate methods for the detection of hydrocarbon reservoir. Finite element method (FEM) is chosen for the modelling of seabed logging to get more precise EM response from hydrocarbon reservoir below 4000 m from seabed. FEM allows to investigate the total electric and magnetic fields instead of scattered electric and magnetic fields, which shows accurate and precise resistivity contrast below the seabed. From the modelling results, It was investigated that Hz field shows higher magni- tude with 342% than the Ex field. It was observed that 0.125 Hz frequency can be able to show better resistivity contrast of Hz field (31.30%) and Ex field (16.49%) at target depth of 1000 m below seafloor for our proposed model. Hz and Ex field delineation was found to decrease as target depth increased from 1000 m to 4000 m. At the target depth of 4000 m, no field delineation response was seen from the current electromagnetic (EM) antenna used by the industry. New EM antenna has been used to see the EM response for deep target hydrocarbon detection. It was investigated that novel EM antenna shows better delineation at 4000 m target depth for Ex and Hz field up to 10.3% and 15.1% respectively. Novel EM antenna also shows better Hz phase response (128.4%) than the Ex phase response (38.3%) at the target depth of 4000 m below the seafloor.展开更多
基金the National Natural Science Foundation of China(62273003,12271003)the Open Project of Anhui Province Center for International Research of Intelligent Control of High-end Equipment(IRICHE-01)+4 种基金the Natural Science Foundation of Universities in Anhui Province(2022AH050993)the Startup Foundation for Introduction Talent of AHPU(2021YQQ058)the Royal Society(WM160014,Royal Society Wolfson Research Merit Award)the Royal Society and the Newton Fund(NA160317,Royal Society-Newton Advanced Fellowship)the Royal Society of Edinburgh(RSE1832)for their financial support.
文摘This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument.The first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth conditions.The second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type conditions.In addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true solutions.Lastly,we carry out some numerical experiments to support the theoretical results.
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission(XK100080537)
文摘This paper deals with the mean-square exponential input-to-state stability(exp-ISS)of Euler-Maruyama(EM)method applied to stochastic control systems(SCSs).The aim is to find out the conditions of the exact and EM method solutions to an SCS having the property of mean-square exp-ISS without involving control Lyapunov functions.Second moment boundedness and an appropriate form of strong convergence are achieved under global Lipschitz coeffcients and mean-square continuous random inputs.Under the strong convergent condition,it is shown that the mean-square exp-ISS of an SCS holds if and only if that of the EM method is preserved for suffciently small step size.
基金supported by the National Natural Science Foundation of China(60873099)the Fundamental Research Funds for the Central Universities(2011QNA29)
文摘As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.
基金Supported by Chinese Government SinoProbe Plan(No.SinoProbe-09-02)R&D of Key Instruments and Technologies for Deep Resources Prospecting(No.ZDYZ 2012-1-03)
文摘Calculations of the ElectroMagnetic(EM) response produced by a large horizontal loop placed over layered medium are rather complex because its integral expression contains the product of two Bessel functions and has a divergent term. In this paper, an improved fast Hankel and Gaver-Stehfest transforms are introduced to solve the strong-oscillation and slow-decay properties of the integrand, where one Bessel function in the product is substituted by a carefully chosen polynomial of high accuracy and the other used as the digital filter coefficients in the convolution integral. Comparisons prove the validity and the efficiency of the proposed method.
文摘This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solution for homogeneous earth and it is used to calculate the secondary electric field in the inhomogeneous Helmholtz Equation. Calculation of Helmholtz Equation is carried out using the finite element method. Validation of this modeling is conducted by comparison of numerical results with 1D analytical response for the case of homogeneous and layered earth. The comparison of CSAMT responses are also provided for 2D cases of vertical contact and anomalous conductive body with the 2D magnetotelluric (MT) responses. The results of this study are expected to provide better interpretation of the 2D CSAMT data.
文摘Deep target hydrocarbon detection is still challenging and expensive. Direct hydrocarbon indicators (DHIs) in seismic data do not correspond to economical hydrocarbon exploration. Due to unreliability in seismic data for the detection of DHIs, new methods have been investigated. Marine controlled source electromagnet (MCSEM) or Sea bed logging (SBL) is new method for the detection of deep target hydrocarbon reservoir. Sea bed logging has also the potential to reduce the risks of DHIs in deep sea environment. Modelling of real sea environment helps to reduce the further risks before drilling the oil wells. 3D electromagnetic (EM) modelling of seabed logging requires more accurate methods for the detection of hydrocarbon reservoir. Finite element method (FEM) is chosen for the modelling of seabed logging to get more precise EM response from hydrocarbon reservoir below 4000 m from seabed. FEM allows to investigate the total electric and magnetic fields instead of scattered electric and magnetic fields, which shows accurate and precise resistivity contrast below the seabed. From the modelling results, It was investigated that Hz field shows higher magni- tude with 342% than the Ex field. It was observed that 0.125 Hz frequency can be able to show better resistivity contrast of Hz field (31.30%) and Ex field (16.49%) at target depth of 1000 m below seafloor for our proposed model. Hz and Ex field delineation was found to decrease as target depth increased from 1000 m to 4000 m. At the target depth of 4000 m, no field delineation response was seen from the current electromagnetic (EM) antenna used by the industry. New EM antenna has been used to see the EM response for deep target hydrocarbon detection. It was investigated that novel EM antenna shows better delineation at 4000 m target depth for Ex and Hz field up to 10.3% and 15.1% respectively. Novel EM antenna also shows better Hz phase response (128.4%) than the Ex phase response (38.3%) at the target depth of 4000 m below the seafloor.
